The thyroid-pituitary homeostatic mechanism

Abstract

The paper develops a mathematical theory of thyroid-pituitary interaction. It is assumed that the pituitary gland produces thyrotropin, which activates an enzyme of the thyroid gland. The rate of production of thyroid hormone is considered to be proportional to the concentration of that enzyme. It is further assumed that in the absence of the thyroid hormone the rate of production of thyrotropin is constant, but, in general, it is a linear function of the concentration of the thyroid hormone. This picture leads to a system of non-linear differential equations, which present great difficulties. This system, however, may be conveniently “linearized”, by considering that the relations between different variables are linear, but that within different ranges of the variables the coefficients are different. Using this approximation, it is possible to show that the system admits periodic solutions of the nature of relaxation oscillations.

Such oscillations are actually observed in some mental disorders, such as periodic catatonia. The study of the effects of different parameters of the system suggests different possible approaches to clinical treatment. In the light of this theory, the experimental determination of the parameters of the system becomes desirable and important.